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generalized_hypergeometric_function [2015/12/16 15:50] nikolaj |
generalized_hypergeometric_function [2015/12/16 15:51] nikolaj |
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| === Discussion === | === Discussion === | ||
| == Definition == | == Definition == | ||
| - | Regarding the coefficient, we could also write | + | The coefficient can more explicitly written as |
| $c_n = \prod_{m=0}^{n-1}\dfrac{1}{(1+m)}\dfrac{\prod_{k=1}^p(a_k+m)}{\prod_{j=1}^q(b_j+m)}$ | $c_n = \prod_{m=0}^{n-1}\dfrac{1}{(1+m)}\dfrac{\prod_{k=1}^p(a_k+m)}{\prod_{j=1}^q(b_j+m)}$ | ||
| - | or write down those products in terms of Gamma functions. | + | or written down in Terms of Gamma functions. |
| The version I chose above seems most elementary to me. | The version I chose above seems most elementary to me. | ||
| - | We used the [[rising factorial]] | + | Above we used the [[rising factorial]] |
| $x^{\overline{n}} := x^{\overline{n},1}$, | $x^{\overline{n}} := x^{\overline{n},1}$, | ||
